Feasible Vectors Research Articles

Method of centers algorithm for multi-objective programming problems

In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multi-objective programming problems.

Partial Gröbner Bases for Multiobjective Integer Linear Optimization

This paper presents a new methodology for solving multiobjective integer linear programs (MOILP) using tools from algebraic geometry. We introduce the concept of partial Gröbner basis for a family of multiobjective programs where the right-hand side varies. This new structure extends the notion of Gröbner basis for the single objective case to the case of multiple objectives, i.e., when there is a partial ordering instead of a total ordering over the feasible vectors. The main property of these bases is that the partial reduction of the integer elements in the kernel of the constraint matrix by the different blocks of the basis is zero. This property allows us to prove that this new construction is a test family for a family of multiobjective programs. An algorithm “á la Buchberger” is developed to compute partial Gröbner bases, and two different approaches are derived, using this methodology, for computing the entire set of Pareto-optimal solutions of any MOILP problem. Some examples illustrate the application of the algorithm, and computational experiments are reported on several families of problems.

Production of biologically active human lymphotactin (XCL1) by Lactococcus lactis

Lymphotactin-XCL1 is a chemokine produced mainly by activated CD8+ T-cells and directs migration of CD4+ and CD8+ lymphocytes and natural killer (NK) cells. We expressed human lymphotactin (LTN) by the lactic-acid bacterium Lactococcus lactis. Biological activity of LTN was confirmed by chemo-attraction of human T-cells by chemotaxis demonstrating, for the first time, how this chemokine secreted by a food-grade prokaryote retains biological activity and chemoattracts T lymphocytes. This strain thus represents a feasible well-tolerated vector to deliver active LTN at a mucosal level.

Concave programming for minimizing the zero-norm over polyhedral sets

Given a non empty polyhedral set, we consider the problem of finding a vector belonging to it and having the minimum number of nonzero components, i.e., a feasible vector with minimum zero-norm. This combinatorial optimization problem is NP-Hard and arises in various fields such as machine learning, pattern recognition, signal processing. One of the contributions of this paper is to propose two new smooth approximations of the zero-norm function, where the approximating functions are separable and concave. In this paper we first formally prove the equivalence between the approximating problems and the original nonsmooth problem. To this aim, we preliminarily state in a general setting theoretical conditions sufficient to guarantee the equivalence between pairs of problems. Moreover we also define an effective and efficient version of the Frank-Wolfe algorithm for the minimization of concave separable functions over polyhedral sets in which variables which are null at an iteration are eliminated for all the following ones, with significant savings in computational time, and we prove the global convergence of the method. Finally, we report the numerical results on test problems showing both the usefulness of the new concave formulations and the efficiency in terms of computational time of the implemented minimization algorithm.

Convergent Lagrangian heuristics for nonlinear minimum cost network flows

We consider the separable nonlinear and strictly convex single-commodity network flow problem (SSCNFP). We develop a computational scheme for generating a primal feasible solution from any Lagrangian dual vector; this is referred to as early primal recovery. It is motivated by the desire to obtain a primal feasible vector before convergence of a Lagrangian scheme; such a vector is not available from a Lagrangian dual vector unless it is optimal. The scheme is constructed such that if we apply it from a sequence of Lagrangian dual vectors that converge to an optimal one, then the resulting primal (feasible) vectors converge to the unique optimal primal flow vector. It is therefore also a convergent Lagrangian heuristic, akin to those primarily devised within the field of combinatorial optimization but with the contrasting and striking advantage that it is guaranteed to yield a primal optimal solution in the limit. Thereby we also gain access to a new stopping criterion for any Lagrangian dual algorithm for the problem, which is of interest in particular if the SSCNFP arises as a subproblem in a more complex model. We construct instances of convergent Lagrangian heuristics that are based on graph searches within the residual graph, and therefore are efficiently implementable; in particular we consider two shortest path based heuristics that are based on the optimality conditions of the original problem. Numerical experiments report on the relative efficiency and accuracy of the various schemes.

Proportional QoS adjustment for achieving feasible power allocation in CDMA systems

Resource management is the general topic of the present paper, particularly, we deal with capacity sharing for interference limited wireless networks by power control. Proportional reduction of the signal-to-interference ratio (SIR) requirements is suggested as the control mechanism to accommodate users in the case of overload. For this purpose, we carefully describe the geometrical structure and the asymptotic behavior of the set of feasible power vectors as a proportionality factor tends to its boundaries. In the case that there is no feasible power adjustment, the minimum proportional SIR reduction is determined under general power constraints. We conclude with developing a locally quadratic convergent algorithm for numerical computation of the optimum power assignment. The investigations provide both insight into the theoretical structure of optimum power allocation as well as a practical method for call admission control.

Transfer of human artificial chromosome vectors into stem cells

Human chromosome fragments and human artificial chromosomes (HAC) represent feasible gene delivery vectors via microcell-mediated chromosome transfer. Strategies to construct HAC involve either ‘build up’ or ‘top-down’ approaches. For each approach, techniques for manipulating HAC in donor cells in order to deliver HAC to recipient cells are required. The combination of chromosome fragments or HAC with microcell-mediated chromosome transfer has facilitated human gene mapping and various genetic studies. The recent emergence of stem cell-based tissue engineering has opened up new avenues for gene and cell therapies. The task now is to develop safe and effective vectors that can deliver therapeutic genes into specific stem cells and maintain long-term regulated expression of these genes. Although the transfer-efficiency needs to be improved, HAC possess several characteristics that are required for gene therapy vectors, including stable episomal maintenance and the capacity for large gene insets. HAC can also carry genomic loci with regulatory elements, which allow for the expression of transgenes in a genetic environment similar to the natural chromosome. This review describes the lessons and prospects learned, mainly from recent studies in developing HAC and HAC-mediated gene expression in embryonic and adult stem cells, and in transgenic animals.

A “Super” Folk Theorem for dynastic repeated games

We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n ≥ 4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.”

Cost Optimization of Reinforced Earth Walls

This paper deals with optimum cost (objective function) design of geosynthetic reinforced earth retaining walls subjected to static and dynamic loading. The design restrictions are imposed as design constraints in the analysis. Choice of the initial designed length and strength of the reinforcement, which are the elements of the design vectors are made in a way that it forms an initial feasible design vector. Thus the problem is one of mathematical programming. The constraints and the objective function being nonlinear in nature, the Sequential Unconstrained Minimization Technique (SUMT) has been used in conjunction with conjugate direction and quadratic fit methods for multidimensional and unidirectional minimization to arrive at the optimal (minimum) cost of the reinforced earth wall. Optimal cost tables are presented for different combinations of the loading and the developed procedure is validated by taking up an example problem. It has been found from the typical example problem that saving of the order of 7–8% can be made over the conventional design of mechanically stabilized earth (MSE) walls with the aid of design charts.

Vector Equilibrium Problems, Minimal Element Problems and Least Element Problems

In this paper we introduce some concepts of feasible sets for vector equilibrium problems and some classes of Z-maps for vectorial bifunctions. Under strict pseudomonotonicity assumptions, we investigate the relationship between minimal element problems of feasible sets and vector equilibrium problems. By using Z-maps, we further study the least element problems of feasible sets for vector equilibrium problems. Finally, we prove a generalized sublattice property of feasible sets for vector equilibrium problems associated with Z-maps.

Regularization in Regression with Bounded Noise: A Chebyshev Center Approach

We consider the problem of estimating a vector ${\bf z}$ in the regression model $\mbox{$\mathcal{B}$} = {\bf A} {\bf z} + {\bf w}$, where ${\bf w}$ is an unknown but bounded noise. As in many regularization schemes, we assume that an upper bound on the norm of ${\bf z}$ is available. To estimate ${\bf z}$ we propose a relaxation of the Chebyshev center, which is the vector that minimizes the worst-case estimation error over all feasible vectors ${\bf z}$. Relying on recent results regarding strong duality of nonconvex quadratic optimization problems with two quadratic constraints, we prove that in the complex domain our approach leads to the exact Chebyshev center. In the real domain, this strategy results in a “pretty good” approximation of the true Chebyshev center. As we show, our estimate can be viewed as a Tikhonov regularization with a special choice of parameter that can be found efficiently by solving a convex optimization problem with two variables or a semidefinite program with three variables, regardless of the problem size. When the norm constraint on ${\bf z}$ is a Euclidean one, the problem reduces to a single-variable convex minimization problem. We then demonstrate via numerical examples that our estimator can outperform other conventional methods, such as least-squares and regularized least-squares, with respect to the estimation error. Finally, we extend our methodology to other feasible parameter sets, showing that the total least-squares (TLS) and regularized TLS can be obtained as special cases of our general approach.

Steepest Ascent Tariff Reforms

This paper introduces the concept of a steepest ascent tariff reform for a small open economy. By construction, it is locally optimal in that it yields the highest gain in utility of any feasible tariff reform vector of the same length. Accordingly, it provides a convenient benchmark for the evaluation of the welfare effectiveness of other well known tariff reform rules, as e.g. the proportional and the concertina rules. We develop the properties of this tariff reform, characterize the sources of the potential welfare gains from tariff reform, use it to establish conditions under which some existing reforms are locally optimal, provide geometric illustrations and compare welfare effectiveness of reforms using numerical examples. Moreover, being a general concept, we apply it to the issue of market access and examine its implications. Overall, the paper's contribution lies in presenting a theoretical concept where the focus is upon the size of welfare gains accruing from tariff reforms rather than simply with the direction of welfare effects that has been the concern of the literature.

Efficient Transduction of Common Marmoset (Callithrix jacchus) Hematopoietic and Embryonic Stem Cells Using Foamyvirus Vectors.

Preclinical animal models are important for evaluating the safety and therapeutic efficacy of new therapeutic modalities such as gene therapy. From the different large animal models, nonhuman primate models have emerged over the last decades as highly desirable experimental systems from both a pathophysiologic and pharmacokinetic viewpoint and the study of nonhuman primates has provided important information on the efficacy and safety of gene therapy systems in vivo prior to human trials. The common marmoset (Callithrix jacchus) has the advantage that it is a small, and thus relatively inexpensive nonhuman primate model. Currently, very little data on the transduction efficiency of foamyviral vectors for gene transfer into marmoset stem cells exists. We therefore performed a direct comparison using identically designed gammaretroviral, lentiviral and foamyviral vector constructs expressing the enhanced green fluorescent protein (EGFP) from the spleen focus forming virus (SFFV) promoter pseudotyped with either the modified human foamy virus (HFV) envelope EM140 or the G-protein of vesicular stomatitis virus (VSV-G) for the transduction of common marmoset embryonic stem cells (CMES) as well as marmoset CD34+ hematopoietic progenitor cells. Virus stocks of these vectors were prepared by polyethyleneimine-mediated transfection of 293T cells and concentrated approximately 10-fold by centrifugation for 4 hours at 10.000 g at 4°C. Three different target cell populations were transduced:common marmoset embryonic stem cells (CMES) or cryopreserved CD34-enriched cells from bone marrow of a common marmoset eitherafter a two-day prestimulation in the presence of IL-6, FLT3L, cSCF and TPO at a concentration of 100 ng/mL each, orafter overnight incubation with 100 ng/mL SCF only.Equal numbers of cells were exposed to the four different vector preparations for 14 hours in 12-well dishes coated with CH-296. The read-out was based on fluorescence microscopy of colonies plated in methyl cellulose as well as flow cytometry (FACS). Foamyviral vectors with the foamyviral envelope were the most efficient gene transfer tool for marmoset hematopoietic CD34-positive cells with stable transduction rates of over 80% as assessed by flow cytometry at both 2 or 7 days after the end of transduction and on average 88% transduction efficiency into colony forming cells (CFU-C). Transduction of CFU-C with all other vector preparations was below 60%. In CMES, initial gene transfer rates of over 80% were achieved with the VSV-G pseudotype lentiviral vector, however, expression decreased to 13% after 7 days. In contrast, the foamyviral vector pseudotyped with the foamyviral envelope decreased only from 49% to 24% after 7 days. In conclusion, we achieved stable viral gene transfer and expression in CMES cells as well as highly efficient gene transfer into common marmoset hematopoietic CD34 positive cells using foamyviral vectors. These results suggest that foamyviral vectors may be highly feasible vectors for stem cell gene transfer and thus set the stage for a more detailed analysis of this vector system in transplantation studies in this nonhuman primate model.

Tabu Search-Based Algorithm for Large Scale Crew Scheduling Problems

<p>In this paper, the problem of finding a work schedule for airline crew members in a given time horizon is tackled. This problem is known in the literature as airline crew scheduling. The objective is to define the minimum cost schedules where each crew, associated to a combination of commercial flights or "legs" called "pairing", is assigned to one or more flights ensuring that the whole set of flights is covered by crew members. The crew scheduling problem can be modeled by using the set covering formulation. This paper presents a new algorithm whose centerpiece is a primal-to-dual scheme aimed at linking any primal solution to the dual feasible vector that best reflects the quality of the primal solution. This new mechanism is used to intertwine a tabu search based, primal intensive, scheme with a lagrangian based, dual intensive, scheme to design a primal-dual algorithm that progressively reduces the gap between upper and lower bound. The algorithm has been tested on benchmark problems from the literature. In this paper, results on real-world airline instances are presented: out of six well-known problems, the algorithm is able to match the optimal solution for four of them while for the last two, whose optimal solution is not known, a new best known solution is found.</p>

The Transport Capacity of Wireless Networks Over Fading Channels

We consider networks consisting of nodes with radios, and without any wired infrastructure, thus necessitating all communication to take place only over the shared wireless medium. The main focus of this paper is on the effect of fading in such wireless networks. We examine the attenuation regime where either the medium is absorptive, a situation which generally prevails, or the path loss exponent is greater than 3. We study the transport capacity, defined as the supremum over the set of feasible rate vectors of the distance weighted sum of rates. We consider two assumption sets. Under the first assumption set, which essentially requires only a mild time average type of bound on the fading process, we show that the transport capacity can grow no faster than O(n), where n denotes the number of nodes, even when the channel state information (CSI) is available noncausally at both the transmitters and the receivers. This assumption includes common models of stationary ergodic channels; constant, frequency-selective channels; flat, rapidly varying channels; and flat slowly varying channels. In the second assumption set, which essentially features an independence, time average of expectation, and nonzeroness condition on the fading process, we constructively show how to achieve transport capacity of /spl Omega/(n) even when the CSI is unknown to both the transmitters and the receivers, provided that every node has an appropriately nearby node. This assumption set includes common models of independent and identically distributed (i.i.d.) channels; constant, flat channels; and constant, frequency-selective channels. The transport capacity is achieved by nodes communicating only with neighbors, and using only point-to-point coding. The thrust of these results is that the multihop strategy, toward which much protocol development activity is currently targeted, is appropriate for fading environments. The low attenuation regime is open.

Tree-width and the Sherali–Adams operator

We describe a connection between the tree-width of graphs and the Sherali–Adams reformulation procedure for 0/1 integer programs. For the case of vertex packing problems, our main result can be restated as follows: let G be a graph, let k⩾1 and let x ̂ ∈R V(G) be a feasible vector for the formulation produced by applying the level- k Sherali–Adams algorithm to the edge formulation for STAB( G). Then for any subgraph H of G, of tree-width at most k, the restriction of x̂ to R V( H) is a convex combination of stable sets of H.

The inverse optimal value problem

This paper considers the following inverse optimization problem: given a linear program, a desired optimal objective value, and a set of feasible cost vectors, determine a cost vector such that the corresponding optimal objective value of the linear program is closest to the desired value. The above problem, referred here as the inverse optimal value problem, is significantly different from standard inverse optimization problems that involve determining a cost vector for a linear program such that a pre-specified solution vector is optimal. In this paper, we show that the inverse optimal value problem is NP-hard in general. We identify conditions under which the problem reduces to a concave maximization or a concave minimization problem. We provide sufficient conditions under which the associated concave minimization problem and, correspondingly, the inverse optimal value problem is polynomially solvable. For the case when the set of feasible cost vectors is polyhedral, we describe an algorithm for the inverse optimal value problem based on solving linear and bilinear programming problems. Some preliminary computational experience is reported.

Ellipsoidal parameter or state estimation under model uncertainty

Ellipsoidal outer-bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown-but-bounded state perturbations and measurement noise. The technique described in this paper applies to linear discrete-time dynamic systems; it can also be applied to weakly non-linear systems if non-linearity is replaced by uncertainty. Many difficulties arise because of the non-convexity of feasible sets. Combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis. Analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented, which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids. The results obtained for combined quadratic constraints are extended to other types of model uncertainty.

Fuzzy Waste Load Allocation Model: Simulation-Optimization Approach

The problem of waste load allocation (WLA) for water quality management of a river system is addressed with a simulation-optimization approach. The WLA model developed in the study provides the best compromise solutions to the pollution control agency (PCA) responsible for maintaining the water quality and the dischargers disposing pollutants into the river system. A previously developed fuzzy waste load allocation model (FWLAM) is extended to incorporate QUAL2E, a water quality simulation model developed by the U.S. Environmental Protection Agency for modeling the pollutant transport in a river. The imprecision associated with establishing water quality standards and the aspirations of the PCA and dischargers are quantified using fuzzy goals with appropriate membership functions. The membership functions of the fuzzy goals represent the variation of the goal satisfaction in the system. A genetic algorithim (GA) is used as an optimization tool to find optimal fraction removal levels to the dischargers and the corresponding satisfaction level. Because a GA is an unconstrained optimization tool, it is extended to handle constraints by complementing it with homomorphous mapping (HM), a constraint handling method for evolutionary algorithms. The GA directs the decision vector in an encoded form to HM. HM, after a few interactions with QUAL2E, redirects the decoded solution back to the GA. The GA assigns a fitness value to the feasible solution vector and applies operators to refine the solution. This interaction among the GA, HM, and QUAL2E continues until a prespecified criterion for global optimality is met. Application of the model is illustrated with a case study of the Tunga-Bhadra River in South India.

On Systems of Linear Equations with Nonnegative Coefficients

We consider a system of linear equations with positive coefficients, where the entries of the nonnegative irreducible coefficient matrix depend on a parameter vector. We say that the parameter vector is feasible if there exists a positive solution to this system. A set of all feasible parameter vectors is called the feasibility set. If all the positive entries are log-convex functions, the paper shows that the associated Perron root is log-convex on the parameter set and the l1-norm of the solution is log-convex on the feasibility set. These results imply that the feasibility set is a convex set regardless whether the l1-norm of the solution is bounded by some positive real number or not. Finally, we show important applications of these results to wireless communication networks and prove some other interesting results for this special case.